A344514 a(n) = Sum_{k=1..n} floor(n/k^2)^k.

1, 2, 3, 5, 6, 7, 8, 12, 14, 15, 16, 22, 23, 24, 25, 34, 35, 43, 44, 54, 55, 56, 57, 69, 71, 72, 92, 106, 107, 108, 109, 140, 141, 142, 143, 199, 200, 201, 202, 222, 223, 224, 225, 247, 309, 310, 311, 400, 402, 434, 435, 461, 462, 554, 555, 583, 584, 585, 586, 616, 617

Offset

1,2

Links

Table of n, a(n) for n=1..61.

Example

a(9) = Sum_{k=1..9} floor(9/k^2)^k = 9^1 + 2^2 + 1^3 = 14.

Mathematica

Table[Sum[Floor[n/k^2]^k, {k, n}], {n, 100}]

Prog

(Python)
from math import isqrt
def A344514(n):
    c, j = 0, 1
    while (j2:=j**2) <= n:
        k = n//j2
        m = isqrt(n//k)
        c += (k**(m+1)-k**j)//(k-1) if k>1 else m-j+1
        j = m+1
    return c # Chai Wah Wu, May 17 2026

Crossrefs

Cf. A013936.

Sequence in context: A394263 A104452 A335073 * A394264 A062877 A068526

Adjacent sequences: A344511 A344512 A344513 * A344515 A344516 A344517

Keyword

nonn

Author

Wesley Ivan Hurt, May 21 2021

Status

approved